Simplify the following expression: $x = \dfrac{-8r^2 + 16r + 24}{r - 3} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-8$ , so we can rewrite the expression: $ x =\dfrac{-8(r^2 - 2r - 3)}{r - 3} $ Then we factor the remaining polynomial: $r^2 {-2}r {-3} $ ${-3} + {1} = {-2}$ ${-3} \times {1} = {-3}$ $ (r {-3}) (r + {1}) $ This gives us a factored expression: $\dfrac{-8(r {-3}) (r + {1})}{r - 3}$ We can divide the numerator and denominator by $(r + 3)$ on condition that $r \neq 3$ Therefore $x = -8(r + 1); r \neq 3$